Change Base Color of Paint Slot, or Delete Paint Slot
You can change the base color.
 
Starting in Blender 2.8, the UV/Image Editor has been separated into two different Editors:

the UV Editor and
the Image Editor

Let's look at you what happens when when you're in Texture Paint Mode and you make a new Texture Slot, and how to change the color later on.
All hyperlinks below link to the Blender v2.83 Documentation.

Setup :
In the following example, I resized the default cube, and sculpted a crude rock.No materials nor textures have been applied. No other changes yet.
 
1st step, Add a Base Color to the Texture Slot :
In the following picture, I have four Editors open in four Areas1,

Image Editor
3D Viewport in Texture Paint mode
Outliner in the upper right
and the Properties Editor


Look at the Properties Editor.
Under the Texture Slots Panel, it says &quot;No Textures&quot; by default. Click the [+] button and click &quot;Base Color&quot; in the Context Menu. You can click the field for &quot;Color&quot; and select the base color for the Texture Paint Slot from the Color Wheel (shown in this next image).

Not shown in picture: I then renamed the Texture Paint Slot &quot;Base Color for TexturePaintSlot&quot;, to make it apparent when we find it later.


2nd step, Find where this color data was saved :
We can now see that the mesh is displayed with a different color in the 3D Viewport's Texture Paint mode. We see this same color in the preview square to the left of our newly created Texture Slot, but it is nowhere else in the entire Properties Editor.
So where is this information stored?


If you don't have one already, open an Outliner Editor.


Once the Outliner is open, click the &quot;Display Mode&quot; button in the Editor's Header (next to the &quot;Editor Type&quot; Button) and select either Blender File or Data API. Each are shown in the following image.
Here we see the name we typed (&quot;Base Color for TexturePaintSlot&quot;)
nested under Images.
The data we just created for the Texture Slot is an Image.



3rd step, Change the Color :
Open the Image Editor and click the dropdown for &quot;Browse Image to be linked&quot; and select the name of the Texture Paint Slot created in the 1st step above.
Note, this means you are &quot;linking&quot; the image into the Image Editor. Similar to how if you change Scenes using the Topbar2, the tooltip displays &quot;Browse Scene to be linked&quot;. If you'd like to know more, read about Data-Block Menus3.

To change the color of our Texture Paint Slot image data:

Change the Image Editor's mode to Paint.
Select the Fill tool in the Toolbar.
Change the color for the tool.
Click on the image.




Concluding Remarks :
It would be nice if we were able to change the color by clicking that little preview square in the Texture Slots Panel, especially if you change your mind and just wanted to make a small tweak.
But for now this is a fairly straightforward way to change the base color (once you understand how the datatype works).
If you'd like to non-destructively change the color, simply go back to the 1st step above, add a new Texture Paint Slot, and select it in that Texture Slots panel. Then follow the rest of the steps and modify your new slot instead.

Links to Blender v2.83 Documentation for further reading :
Areas1 : 
docs.blender.org/manual/en/2.83/interface/window_system/areas.html
Topbar2 : 
docs.blender.org/manual/en/2.83/interface/window_system/introduction.html
Data-Block Menus3 : 
docs.blender.org/manual/en/2.83/interface/controls/templates/data_block.html#ui-data-block